reserve X for TopSpace;
reserve C for Subset of X;
reserve A, B for Subset of X;
reserve X for non empty TopSpace;
reserve Y for extremally_disconnected non empty TopSpace;

theorem Th43:
  D-Union Y = OPD-Union Y & D-Meet Y = OPD-Meet Y
proof
A1: Domains_of Y = Open_Domains_of Y by Th42;
  hence D-Union Y = (D-Union Y)||Open_Domains_of Y by RELSET_1:19
    .= OPD-Union Y by TDLAT_1:42;
  thus D-Meet Y = (D-Meet Y)||Open_Domains_of Y by A1,RELSET_1:19
    .= OPD-Meet Y by TDLAT_1:43;
end;
